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dx is the width of each strip. dx would then be the width of the first strip. Δx is the width of a finite number of strips, which is not what I am looking for.

It has to be along a distance dx.

Doh. The area of that first strip would be the height (F0) by the width (dx.) Ok problem solved.

An upper limit of dx would be the area of the first strip of dx. I need to prove the above.

The integral comes from finding the work done by a force over a distance dx. The force may or may not be variable so I needed to prove the variableness of F did not matter over an infinitesimal for the purposes of determining the amount of work done. So dw = F⋅dx => F0⋅dx So integrating over...

Ok so what I want to know is, is this valid? If so what does it mean?